There seems to be some dispute about this and it could be based on model and year, but in general the charge port of a locked car will open when a nearby Tesla charge plug button is pressed. Thus, some people will plug in another's Tesla who is abusing the charging network by using it as special reserved parking for themselves.
While it's a cute approach that has been around for a long time, I am not sure it is the best practice to plug another's car in. First, some spots have signage that allow general parking (indefinitely, up to 30 minutes, etc). In that case, the non-charging Tesla is no different than an ICE vehicle permissibly parking. Second, Tesla's now have sentry mode. The owner of that Tesla could be angry at being plugged in and potentially seek out police to press charges against you for violating their property. I have not heard of this happening, but it's a thought (especially if the spot is general parking).
It may be best to leave a nice note.
All of that being said, I agree with the OP that Tesla's who take up charging spots are jerks. Especially in this location where there is ample parking adjacent that is never crowded. And, as the OP noted he/she is taking up the one Model X w/ trailer spot.